sdss-iv manga: bulge–disc decomposition of ifu data cubes … · 2017-02-18 · evelyn j....

MNRAS 465, 2317–2341 (2017) doi:10.1093/mnras/stw2823Advance Access publication 2016 November 3

SDSS-IV MaNGA: bulge–disc decomposition of IFU data cubes (BUDDI)

Evelyn J. Johnston,1,2‹ Boris Haußler,1,3,4 Alfonso Aragon-Salamanca,2

Michael R. Merrifield,2 Steven Bamford,2 Matthew A. Bershady,5 Kevin Bundy,6

Niv Drory,7 Hai Fu,8 David Law,9 Christian Nitschelm,10 Daniel Thomas,11

Alexandre Roman Lopes,12 David Wake5,13 and Renbin Yan14

1European Southern Observatory, Alonso de Cordova 3107, Casilla 19001, Santiago, Chile2School of Physics and Astronomy, University of Nottingham, University Park, Nottingham NG7 2RD, UK3University of Oxford, Denys Wilkinson Building, Keble Road, Oxford, Oxon OX1 3RH, UK4University of Hertfordshire, Hatfield, Hertfordshire AL10 9AB, UK5Department of Astronomy, University of Wisconsin–Madison, 475 N. Charter Street, Madison, WI 53706-1582, USA6Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced Study, The University of Tokyo,Kashiwa, Chiba 277-8583, Japan7McDonald Observatory, University of Texas at Austin, Austin, TX 78712, USA8Department of Physics & Astronomy, University of Iowa, Iowa City, IA 52245, USA9Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA10Unidad de Astronomıa, Universidad de Antofagasta, Avenida Angamos 601, Antofagasta 1270300, Chile11Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 3FX, UK12Departamento de Fısica, Facultad de Ciencias, Universidad de La Serena, Cisternas 1200, La Serena, Chile13Department of Physical Sciences, The Open University, Milton Keynes MK7 6AA, UK14Department of Physics and Astronomy, University of Kentucky, 505 Rose Street, Lexington, KY 40506, USA

Accepted 2016 November 1. Received 2016 November 1; in original form 2016 April 23

ABSTRACTWith the availability of large integral field unit (IFU) spectral surveys of nearby galaxies, thereis now the potential to extract spectral information from across the bulges and discs of galaxiesin a systematic way. This information can address questions such as how these componentsbuilt up with time, how galaxies evolve and whether their evolution depends on other propertiesof the galaxy such as its mass or environment. We present bulge–disc decomposition of IFUdata cubes (BUDDI), a new approach to fit the two-dimensional light profiles of galaxies as afunction of wavelength to extract the spectral properties of these galaxies’ discs and bulges.The fitting is carried out using GALFITM, a modified form of GALFIT which can fit multiwavebandimages simultaneously. The benefit of this technique over traditional multiwaveband fits is thatthe stellar populations of each component can be constrained using knowledge over the wholeimage and spectrum available. The decomposition has been developed using commissioningdata from the Sloan Digital Sky Survey-IV Mapping Nearby Galaxies at APO (MaNGA) surveywith redshifts z < 0.14 and coverage of at least 1.5 effective radii for a spatial resolution of2.5 arcsec full width at half-maximum and field of view of > 22 arcsec, but can be appliedto any IFU data of a nearby galaxy with similar or better spatial resolution and coverage.We present an overview of the fitting process, the results from our tests, and we finish withexample stellar population analyses of early-type galaxies from the MaNGA survey to give anindication of the scientific potential of applying bulge–disc decomposition to IFU data.

Key words: galaxies: bulges – galaxies: evolution – galaxies: formation – galaxies: stellarcontent – galaxies: structure.

1 IN T RO D U C T I O N

The assembly history of a galaxy can be studied through its stel-lar populations – the spectral features provide information about

� E-mail: [email protected]

the star formation history of the galaxy, while the spatial distribu-tion of the different stellar populations gives clues as to how theyhave been redistributed throughout the galaxy during mergers andsecular processes. Components such as the bulge and disc formedthrough different mechanisms, and thus have experienced funda-mentally different star formation histories (Seigar & James 1998;MacArthur, Courteau & Holtzman 2003; Allen et al. 2006; Cameron

C© 2016 The AuthorsPublished by Oxford University Press on behalf of the Royal Astronomical Society

at University of Portsm

outh Library on January 6, 2017

http://mnras.oxfordjournals.org/

Dow

nloaded from

mailto:[email protected]


2318 E. J. Johnston et al.

et al. 2009; Simard et al. 2011). Consequently, many studies havetried to separate the light from the bulge and disc to better under-stand their formation and contribution to the evolution of the hostgalaxy.

One first step towards a complete decomposition of a galaxy isits separation into its two main components, the bulge and disc.So-called bulge–disc decomposition can be carried out in twoways: through one-dimensional surface brightness profile fitting(Kormendy 1977; Burstein 1979; Kent 1985), in which the radiallyaveraged light profile is fitted after correcting for the inclination ofthe galaxy, or two-dimensional fitting of images of galaxies (Shaw& Gilmore 1989; Byun & Freeman 1995; de Jong 1996a). Both tech-niques provide information on the colours, sizes and luminosities ofeach component included in the fit, which provide constraints on themasses, ages and metallicities of each component (Pforr, Maraston& Tonini 2012). For example, as part of the Fundamental Plane, ithas been found that in elliptical galaxies and bulges of disc galax-ies the scalelengths increase and the effective surface brightnessesdecrease with increasing luminosity (Kormendy 1977; Djorgovski& Davis 1987; Hamabe & Kormendy 1987). These results suggestthat both structures have experienced similar star-formation histo-ries, despite the differing presence or absence of a dynamically colddisc in the host galaxies. However, while the same trend has beendetected in the bulges of field S0s, it is not always present in clusterS0s, thus indicating that the local environment plays a significantrole in the formation of S0 bulges (Barway et al. 2009).

It has also been found that as you move from S0s to late-typespirals, the effective size and surface brightness of the bulge de-crease, whereas discs in these galaxies display much less varia-tion in these properties between morphologies (de Jong 1996b;Graham 2001; Mollenhoff & Heidt 2001; Trujillo et al. 2002;Aguerri et al. 2004; Laurikainen et al. 2007; Graham & Wor-ley 2008; Oohama et al. 2009). As a result, it is becoming apparentthat the increase in the bulge-to-total (B/T) light ratio observed inS0s is driven by the evolution of the bulge as opposed to simply thefading of the disc.

In recent years, bulge–disc decomposition has been increasinglyapplied to multiwaveband photometry since the bulge and disccolours can act as a proxy for their stellar populations. Comparisonof bulge and disc colours has shown that in both spirals and S0s,the discs are bluer than the bulges (Bothun & Gregg 1990; Peletier& Balcells 1996; Hudson et al. 2010; Head et al. 2014), suggestingthat disc galaxies have more recent star formation activity at largerradii (de Jong 1996b) or higher metallicities in their nuclear regions(Beckman et al. 1996; Pompei & Natali 1997). This method has alsorevealed negative colour gradients within both the bulges and discsof disc galaxies (Terndrup et al. 1994; Peletier & Balcells 1996;Michard & Poulain 2000; Mollenhoff 2004; Kannappan, Guie &Baker 2009; Head et al. 2014). Since negative colour gradients im-ply that redder light is more centrally concentrated within thesecomponents than bluer light, such trends imply the presence of in-creasingly older or more metal-rich stellar populations at smallerradii within these galaxies.

Traditionally, multiwaveband bulge–disc decomposition has beencarried out on each image independently (e.g. Pahre, Djorgovski &de Carvalho 1998a; Pahre, de Carvalho & Djorgovski 1998b; Ko& Im 2005; La Barbera et al. 2010; Lange et al. 2015). While thisapproach works in general, it is susceptible to poor fits in casesof low signal to noise, which can affect the analysis of the results.Some groups have tried to combat this issue. For example, Lackner& Gunn (2012) used the decomposition parameters obtained fromfitting the r-band image of each galaxy to constrain all the fitting

parameters except the flux in all other wavebands. However, thisapproach still gives no information about how the sizes and ori-entations of each component vary with wavelength. An alternativesolution was used by Simard et al. (2002, 2011), who were able toapply a simultaneous galaxy profile fit to two images, and Mendelet al. (2014), who showed similar results for different pairs of wave-band combinations. These simultaneous fits were constrained suchthat only the total flux, B/T light ratio and background level wereallowed to vary between bands, and the images at each wavebandwere fitted simultaneously with the r-band image, which is the deep-est image. As a result, while they provide a better fit to the bulge anddisc components, the fits are dominated by the r-band parameters.

As a result of these issues, the ‘MegaMorph’ project has devel-oped GALFITM1 (Haußler et al. 2013), a modified version of GALFIT2

(Peng et al. 2002, 2010) that can decompose an arbitrary numberof multiwaveband images simultaneously. Vika et al. (2014) foundthat multiwaveband decompositions with GALFITM improve the re-liability of measurements of the component colours, and thus theircolour gradients. However, estimates of the ages and metallicities ofstellar populations derived from colours alone are highly degenerate(Worthey 1994), and can also be affected by dust reddening (Disney,Davies & Phillipps 1989). Therefore, to better understand the star-formation histories across galaxies, the addition of spectroscopicinformation is vital.

A spectroscopic bulge–disc decomposition technique was devel-oped by Johnston et al. (2012) and Johnston, Aragon-Salamanca &Merrifield (2014), in which long-slit spectra along the major axesof S0s were decomposed into bulge and disc components. Thesestudies fitted the one-dimensional light profiles as a function ofwavelength, and then used integration of these profiles to obtain theglobal bulge and disc spectra for each galaxy. A different approach todecomposing long-slit spectra of S0s was used by Sil’chenko et al.(2012), who first decomposed Sloan Digital Sky Survey (SDSS)images of each galaxy, and used the bulge and disc effective radiito determine the bulge and disc-dominated regions of the galaxy.They took a spectrum for the bulge at a radius of 0.5 bulge effectiveradii, and subtracted off a disc spectrum that was measured from thedisc-dominated region and scaled according to the B/T light ratiofrom the photometric decomposition. All three studies found thatthe bulge regions of S0s contain systematically younger and moremetal-rich stellar populations, but with long-slit spectra alone it isimpossible to determine whether these young stellar populations aredistributed throughout the bulge, or are concentrated in the centreof the disc.

With the introduction of wide-field integral-field spectroscopicinstruments, such as VLT/MUSE (Bacon et al. 2010), and sur-veys, such as the Calar Alto Legacy Integral Field spectroscopyArea (CALIFA; Sanchez et al. 2012) and the SDSS-IV MappingNearby Galaxies at Apache Point Observatory (MaNGA; Bundyet al. 2015), it is now possible to apply bulge–disc decompositionto three-dimensional spectroscopic data. One such study has suc-cessfully separated the bulge and disc stellar populations of S0sin CALIFA kinematically (Tabor et al., in preparation). We havedeveloped a complementary approach called Bulge–Disc Decom-position of Integral field unit (IFU) data cubes, or BUDDI, which usesGALFITM to decompose the light profiles of galaxies in an IFU datacube into multiple components, giving both the integrated spectraand the two-dimensional data cube for each component.

1 http://www.nottingham.ac.uk/astronomy/megamorph/2 https://users.obs.carnegiescience.edu/peng/work/galfit/galfit.html

MNRAS 465, 2317–2341 (2017)




Dow

nloaded from

http://www.nottingham.ac.uk/astronomy/megamorph/

https://users.obs.carnegiescience.edu/peng/work/galfit/galfit.html


Bulge–disc decomposition of IFU data cubes 2319

In this paper, we present this new method and give an indicationof its potential by applying the technique to a small sample ofgalaxies from the MaNGA survey. Section 2 gives an overview of theMaNGA survey and data, and Section 3 describes the decompositiontechnique. Section 4 looks at various tests that were carried out toensure that the decomposition of the data cubes is reliable andconsistent, and Section 5 describes the initial stellar populationsanalysis of a small number of galaxies. Finally, our conclusions arepresented in Section 6.

2 SU M M A RY O F M aN G A DATA

The decomposition technique presented in this paper was testedon commissioning data observed as part of the MaNGA (Bundyet al. 2015) survey, observed in 2014 March and June with theSloan 2.5 m telescope (Gunn et al. 2006). MaNGA is part of thefourth-generation Sloan Digital Sky Survey (SDSS-IV) that startedon 2014 July 1 for 6 yr, sharing dark time during that period withthe eBOSS Survey (Zhao et al. 2016).

The MaNGA survey aims to study the internal stellar and gaskinematics and stellar population structures of a sample of ∼10 000galaxies in a redshift range of 0.01 < z < 0.15. Up to 17 galaxiescan be observed simultaneously using a series of hexagonal IFUsof different sizes plugged into a plate of 7 deg2. The IFUs rangein size from 19 fibres (12 arcsec diameter on sky) to 127 fibres(32 arcsec), and there are a further 12 mini-bundles of 7 fibres usedto observe standard stars for flux calibration (Yan et al. 2016), and92 single fibres for sky subtraction. Each fibre has a diameter of120 microns (2 arcsec diameter on sky), and feeds into the dualbeam BOSS spectrographs (Smee et al. 2013). 67 per cent of thetotal sample of galaxies are in the Primary sample, and are observedwith the appropriately sized IFU to ensure spatial coverage out to1.5 effective radii in the r band. The Secondary sample, consistingof the remaining 33 per cent, will have spatial coverage out to 2.5effective radii. Both samples cover the same mass range, but theSecondary sample is on average at a slightly higher redshift (〈z〉 =0.045 versus 〈z〉 = 0.030 for the Primary sample). The IFUs providea continuous wavelength coverage between 3600 to 10 300 Å, witha spectral resolution of R ∼ 1400 at 4000 Å to R ∼ 2600 at 9000 Å(Drory et al. 2015).

With a typical integration time per field of 2–3 h, a signal-to-noiseratio (S/N) of 4–8 Å−1 per fibre can be reached in the outskirts ofPrimary sample MaNGA galaxies, using an assumed luminosityin those regions of 23 AB mag arcsec−2. Each field is observedin multiples of three 15 min exposures using a three-point ditherpattern to ensure full spatial coverage between the fibres and toobtain a uniform point spread function (PSF; Law et al. 2015).

The data used in this paper were observed with the 2014 Marchand July commissioning plates, 7443 and 7815, respectively, usingthe 127, 91 and 61-fibre IFUs. Throughout this paper, the galaxieswill be referred to by their plate number-IFU number combination.For example, galaxy 7443-12701 was observed with plate 7443 andthe first of the 127 fibre IFUs. The sample covers the redshift range0.017 < z < 0.14, and covers a wide range of galaxy morphologies.The data were reduced using version v1.5.1 of the MaNGA datareduction pipeline (DRP; Law et al. 2016), and the reduced and fluxcalibrated MaNGA fibre spectra were combined to produce the finaldata cubes. The pixel scale in the data cubes was set to 0.5 arcsec,the PSF was found to have a full width at half-maximum (FHWM)of 2.5 arcsec, and the IFUs have fields of view between 22 and32 arcsec in diameter. The data cubes use a logarithmic wavelengthsolution, providing a wavelength coverage of 3.5589–4.0151 (in

units of logarithmic Angstroms), with a step size of 10−4 dex over4563 spectral elements (Law et al. 2016).

3 BUDDI: BU L G E – D I S C D E C O M P O S I T I O N O FIFU DATA C U B E S

One can see an IFU data cube of a galaxy as simply a stack ofimages at each wavelength step. If the S/N and spatial resolution issufficiently high, features, such as the bulge, disc, spiral arms etc.,can be distinguished in each image. In such cases, it is possible todecompose the data cube of the galaxy wavelength-by-wavelengthto spectroscopically separate the light from each component. If,however, the S/N is lower, and especially when several componentswith different colours are present in the galaxy, this separationis not as easy in each individual wavelength and an approach isneeded that uses all information in the cube/multiwavelength in-formation simultaneously. Such data are ideally set up for imagedecomposition using GALFITM, a modified version of GALFIT3 (Penget al. 2002, 2010) that is able to fit multiwaveband images of galax-ies simultaneously to produce one wavelength-dependent model(Haußler et al. 2013). GALFITM fits user-defined degrees of Cheby-chev polynomials to the variable galaxy parameters to produce asingle, consistent, wavelength-dependent model of a galaxy. Thesepolynomial fits have the additional benefit that the fit to each imageis constrained by the fits of the rest, thus boosting the signal to noiseof the data set over that of any individual image within the set. As aresult, individual images with lower signal to noise only minimallyaffect the wavelength-dependent fit (Vika et al. 2013).

Ideally, one would run the IFU data cube through GALFITM directlyin order to keep the full galaxy information for the fitting process.However, due to the number of images/wavelengths involved, thiswould need a) a lot of memory, as the entire cube, model, etc. haveto be kept in memory at any given time and b) a lot of CPU time,making this approach impossible in practice. If one wants to de-rive the full spectrum of the bulge and disc of a galaxy, each newwavelength adds another two free parameters for the magnitudesof each component, even if the values in all other parameters aresomehow kept the same. With more than 4000 wavelength steps inthe case of a MaNGA data cube, it becomes obvious why this is afutile task. Instead, one has to come up with a different, intermediateapproach. In the development of BUDDI, we decided on a four-stepfitting process in GALFITM, in which some further pre-preparation isincluded. After this preparation, we first fit a broad-band image, inwhich all wavelengths have been combined, then a set of narrow-band images, in which the full data cube has been binned in thewavelength direction in order to get a manageable number of im-ages. Finally, we return to the full wavelength resolution by fittingthe individual wavelength steps in blocks of 30 in order to derivethe full spectra for each galaxy component. This last step could inprinciple also be done individually, but we prefer this approach asit keeps a lower number of images and files on disc and is easierto handle. The outcome, however, should in principle be identical(for more details of the differences between GALFIT and GALFITM,see Bamford et al., in preparation). An overview of this process todecompose a galaxy data cube is shown in Fig. 1, as developed inthis work using MaNGA data. The individual steps are explainedfurther in this section.

3.1 Step 1: data preparation/obliterating kinematics

The first step was to measure and obliterate the kinematics acrossthe galaxy in order to obtain a homogeneous data cube, where each

MNRAS 465, 2317–2341 (2017)




Dow

nloaded from



Figure 1. Overview of the steps to decompose an IFU data cube with BUDDI. The free parameters are the luminosity (L), effective radius (Re), Sersic index (n),PA, axes ratio (q) and residual-sky value (RS), and the suffixes correspond to the bulge (b) and disc (d) components. The colours of each parameter identify howit varies with wavelength – dark blue means it is completely free with wavelength, purple is allowed to vary according to a linear polynomial, light blue can bedifferent for different components, but remains constant with wavelength, and red is held fixed according to the best-fitting polynomial from the previous step.

spaxel in each image slice measures the light at the same rest-framewavelength and at the same position within any spectral feature atthat wavelength. This step ensures that no artificial gradients in anyline strengths are added due to the radial velocity of the stellar discin highly inclined galaxies, or due to the narrowing of the spectralfeatures further from the bulge-dominated region. While decom-position is possible without obliterating the kinematics, it wouldlead to very broad spectral features in the final decomposed spectra,reducing the spectral resolution and blurring together neighbouringfeatures.

The data cubes were spatially binned using the Voronoi bin-ning technique of Cappellari & Copin (2003), and the absorption-line kinematics measured using the Penalized Pixel-Fitting method(PPXF) of Cappellari & Emsellem (2004). At this stage, the wave-lengths of emission features were masked out to exclude them fromthe fits. The kinematics were then measured as offsets from thecentre of the galaxy, which was taken as the point in the centralregion of the galaxy where the velocity dispersion peaked, or wherethe luminosity peaks in the case that the velocity dispersion showsa double-peaked profile with radius. The line-of-sight velocity wascorrected by shifting the spectrum to match that measured at thecentre, and the velocity dispersion was corrected by convolvingeach spectrum with the appropriate Gaussian to bring it up to themaximum measured within that galaxy.

It is important to note at this stage that if strong emission linesare present in the spectrum that do not trace the same kinemat-ics as the absorption features, they will not be corrected to thesame level of accuracy as the absorption spectrum. Large misalign-ments in the kinematics, particularly in cases of counter-rotatinggaseous discs, would lead to contamination of the decomposed spec-tra by artificially broadened emission features. Such an effect can beseen at ∼5577 Å in Fig. 5 where the spectrum contains significant

residuals of a bright sky line. While modelling the emission linesis beyond the scope of this work, it is expected that in future workstrong emission features will be modelled and subtracted reliablyat this stage of the fitting process to reduce their effects on the finaldecomposed spectra.

3.2 Step 2: fitting one broad-band image

Having obliterated the kinematics within the data cube, the galaxycan be fitted with GALFITM. The first step was to median stack theentire data cube into a single, broad-band or white-light image of thegalaxy, and to decompose it with GALFITM. In this first step, however,where only one broad-band image is used for the fit, these multibandfeatures are technically not needed and the normal version of GALFIT

could be used instead. For consistency and in order to only rely onone code, we have chosen to use GALFITM even in this first step.

After creating the broad-band image, a mask was created to iden-tify the zero-value pixels in the image that are outside of the hexag-onal MaNGA IFU field of view. This mask was used in this stepand the subsequent steps to ensure that only those pixels with infor-mation were included in the fits.

The initial fit was carried out using a single Sersic profile and aresidual-sky component, and a PSF image was included for convo-lution. The PSF profile was created by median stacking the broad-band griz-band PSF images for that data cube, which are providedas part of the MaNGA data products. Although no large influenceon the final fitting result was recorded in previous tests, the startingparameters in GALFITM are somewhat important to the fit, especiallyin multicomponent decompositions. As we were unable to find ageneral automatic solution for deriving those starting values, weestimated starting parameters by eye for this first step.

MNRAS 465, 2317–2341 (2017)




Dow

nloaded from



After fitting the broad-band image with GALFITM, the residualimage created by subtracting the model from the original imagewas used to visually identify whether the starting parameters arereasonable and if an additional component would be necessary toimprove the fit. In cases where the latter was true, the fit was repeatedwith an additional Sersic profile. For ease of analysis in this study,the more extended component has been assumed to be the disc,while the more centrally concentrated component has been labelledas the bulge. As a further check of the initial parameters for this fit,we have carried out a similar fit with the same starting parameterson photometric data of the same galaxy (see Section 4.2).

Since the model light profiles created by GALFITM are smooth,any non-smooth features within the galaxy, such as spiral arms orbright knots of star formation within the disc, will not be includedin the model. In the presence of very bright or very large structures,it can happen that they are included in the fit to the bulge or disc,thus artificially enhancing the luminosity of the component. In suchcases, they must therefore be masked from the fit.

3.3 Step 3: fitting narrow-band images

After fitting the broad-band image, the data cube was binned in thewavelength direction to produce a series of narrow-band images.The purpose of this step is to derive the polynomials of most galaxyparameters that describe how they change with wavelength. Thesepolynomials can then be used in the last fitting step to derive the fullspectra of the galaxy components. As long as the number of imagesused here is sufficiently high, it is not necessary to carry out thefitting of these polynomials by using all images at all wavelengths,saving huge amounts of CPU time in the process. In the case of theMaNGA data presented here, it was found that using 30 narrow-band images provided a good balance between S/N, the number ofdata points for the polynomial fits, and the time needed for GALFITM

to fit that many images.The Chebyshev polynomials used by GALFITM are arbitrarily nor-

malized over a range of −1 to 1, which is mapped to the spectralrange of the input data. In order to ensure that the best-fitting poly-nomials for the narrow-band images cover the full spectral rangeof the IFU cube, the first and last narrow-band images must be theimage slices at the start and end wavelengths of the spectral rangecovered, instead of e.g. the centre of the first and last narrow-bandimages. Otherwise, the polynomial coefficients produced by thissecond step cannot be used for the full spectral range in the laststep. Therefore, the 30 narrow-band images consist of 28 median-stacked images plus the first and last image slices of the desiredwavelength range.

For simplicity, the binning of the median-stacked images wasapplied by separating the remaining data cube over the desiredwavelength range into 28 equal regions, and stacking the individualimages within each region to create the narrow-band images. Sincethe data cubes were binned logarithmically in the wavelength direc-tion, each of these stacked images was created from equal numbersof image slices, or channels. In the case of the MaNGA data cubes,using a wavelength range of 3700 < λ < 10 300 Å, each narrow-band image was created by median stacking ∼160 image slices.Therefore, any strong emission features present in the spectra hadonly a small effect on the final narrow-band image. It was not nec-essary to exclude the regions around bright emission features whencreating the binned images since GALFITM uses polynomials to definethe fit parameters, and thus can fit through these affected imagesusing the information from the rest of the wavelength range.

With multiwaveband fits, it is important to account for the wave-length variation in the PSF profile, and so for each narrow-bandimage a PSF image at that wavelength was included. The PSF im-ages corresponding to each narrow-band image were created byinterpolating between the four broad-band griz PSF images.

The images were fit with GALFITM, using the best-fitting modelfrom the broad-band image (from step 1) as the initial parametersfor the multiwaveband fit. For the fits of these narrow-band images,only the luminosities of the bulge and disc (Lb and Ld, respectively)and the residual-sky background were left completely free. Due tothe wealth of the information present in the multiband images andthe constraints between images due to the polynomials used, wefound that this freedom was not a problem as long as the field ofview contained even a small region of sky.

The effective radii of the bulge and disc (Reb and Red, respectively)and their Sersic indices (nb and nd) were constrained to vary linearlyover the wavelength range. The position angle (PA) and axis ratio (q)of each component were assumed to be constant with wavelengthwhile being allowed to be different between the two components.These restrictions on the polynomials for the variables were selectedto improve the fit over the full wavelength range, compensating forindividual image slices with higher levels of noise or contaminationby sky lines, while also allowing enough freedom to look for colourgradients within the bulge and disc, as measured from the gradientsin their effective radii (see e.g. Johnston et al. 2012).

A comparison of the constrained and free fits, in which all param-eters were given full freedom, to the narrow-band images of galaxy7443-9102 are given in Fig. 2. As a further example, the results fromfitting SDSS griz images in the same way are also overplotted (seeSection 4.2 for more details). It can be seen that the constrained pa-rameters fit well to the unconstrained parameters, thus providing areliable smooth variation with wavelength. Not all galaxies are bestfitted with the constraints listed here (see e.g. Kelvin et al. 2012),and in such cases it may be necessary to allow more freedom in themodels by increasing the orders of the polynomials. In this galaxy,the largest differences between the constrained and free fits are inthe bulge Sersic indices. The most likely reason for this discrep-ancy is likely to be the difference in the spatial resolution – theimaging data has a spatial resolution of ∼1.3 arcsec FWHM whilethe MaNGA images have a resolution of 2.5 arcsec – leading toblurring together of different features and artificial broadening ofcompact sources. Such broadening effects can be seen in the fore-ground objects in Figs 3 and 4, which show examples of the bestfits to the SDSS and MaNGA griz-band images for this galaxy. Theresidual images, which were created by subtracting the best-fittingmodel from the SDSS images, show a bright, compact source oflight at the centre of the galaxy that has not been included in thefit. In the MaNGA data however, this feature appears much fainterand broader in the residual images, typically accounting for about1.9 per cent of the total light in the same region in the original im-ages compared to ∼4.2 per cent in the SDSS griz-band images. Thisresult suggests that the light from this central bright component hasbeen blurred with the bulge light in the MaNGA data, leading to anincrease in the bulge Sersic index due to the brighter centre.

It can also be seen that, in some cases, the free parameter fitsfor the first and last images are very different from the rest of theresults for that parameter. This effect is simply due to these imagesbeing the individual image slices at the start and end wavelengthsof the spectral range, and thus they have lower S/N than the restof the data set and result in poorer fits. It has also been found thatthe S/N at extreme wavelength ranges in MaNGA data tends to belower due to lower throughput in these regions (see e.g. fig 4 of Yan

MNRAS 465, 2317–2341 (2017)




Dow

nloaded from



Figure 2. The decomposition parameters obtained for the narrow-band images of galaxy 7443-9102, showing the results for both the free fits (dots) and theconstrained fits (solid line) using (GALFITM). The two columns represent the results from the bulge (left) and disc (right), and from top to bottom the parametersare the integrated magnitude, the effective radius, the Sersic index, the PA and the minor/major axis ratio. Overplotted as coloured squares, circles and trianglesare the decomposition parameters obtained after fitting the SDSS griz-band images with GALFITM.

et al. 2016). In the constrained fits, these images, in particular, aresupported by neighbouring images, leading to a much more reliablefit even in these images.

3.4 Step 4: fitting individual wavelength images

Having decomposed the narrow-band images and obtained thepolynomials describing the wavelength dependence of the com-ponent parameters, it is now possible to decompose the data cubewavelength-by-wavelength. Due to the computing power needed todecompose the whole data cube in one go, it is again necessary tosplit it up into chunks of, say, 30 image slices. Technically, this stepcould also be carried out wavelength-by-wavelength using GALFIT

single band fitting. However, we chose to fit the blocks of imageswith GALFITM to reduce the number of intermediate files created (i.e.one file created per 30 images instead of per image) and to main-tain consistency by using the same fitting software throughout thewhole process. With the polynomials for all structural parametersalready known from the previous step, it is unnecessary to allow anyfreedom in any of those parameters. Doing so would only introduceartefacts at the wavelengths where the blocks of images meet. Forthis final decomposition, only the bulge and disc luminosities andthe residual-sky value were allowed complete freedom, while all theremaining parameters were held fixed at the values determined ateach wavelength through calculation from the polynomial derivedby the narrow-band fit. While such restrictions do limit the informa-tion that can be obtained, such as the measurement of line strength

gradients within each component, they constrain the fits sufficientlythat each image slice can be decomposed in a consistent way.

Finally, from the resulting luminosities at each wavelength, thedecomposed spectra can be reconstructed in two ways. The first isto simply plot the total luminosity of each component as a functionof wavelength to produce a one-dimensional integrated spectrumfor that component, from which the mean, global stellar popula-tions and star formation histories can be measured. An example ofthe decomposed one-dimensional bulge and disc spectra for galaxy7443-12701 is shown in Fig. 5, along with the original spectrum,the best fit from the combined bulge+disc+residual-sky spectrumoverplotted on the original, the residual-sky component included inthe fit, and finally the residuals after subtracting the best fit from theoriginal. The majority of the regions of poor fits and higher levelsof noise in the fits correspond to regions of non-zero residual-skybackground and poorly subtracted strong sky lines. While the DRPdoes a good job of sky subtraction in the MaNGA data cubes usingthe dedicated sky IFUs, generally to better than Poisson error es-timates, the sky subtraction is not perfect, especially in regions ofstrong sky lines (Law et al. 2016). For example, part of the strong[O I] sky line at 5577.4 Å has been included in the bulge and discmodels, with the remainder of the light at that wavelength appearingin the residuals. Similarly, the increased residuals at redder wave-lengths coincides with the increase in the residual-sky backgroundlevel and the number of sky lines in this region. The skylines shouldin principle mostly contribute to the residual-sky background mea-sured, not the actual profile luminosity. It is reassuring that we dofind the residual-sky background elevated at and around skylines,

MNRAS 465, 2317–2341 (2017)




Dow

nloaded from



Figure 3. Comparison of the decompositon of the SDSS griz images. Thecolumns from left to right show the original griz images for galaxy 7443-9102, the best-fitting model composed of two Sersic profiles, and the residualimages after subtracting the model from the original image. The colourdistributions of all images are linear, with a range of 99.5 per cent of thetotal range in pixel values. The scaling of the residual images has beenadjusted to best show any features present.

as it shows that the simultaneous background estimation in thesefits works, despite the lack of any clean ‘sky’ pixels that are usuallyneeded to reliably determine the residual-sky background level.

The second technique is to use GALFITM to create images of eachcomponent at each wavelength from the decomposition parameters.These images can then be stitched together to produce IFU datacubes representing purely the light from each component. Thesedata cubes can be used to visualize how each component varieswith wavelength, and potentially to study stellar population gra-dients within each component. Such gradients were detected byJohnston et al. (2012) in the decomposition of long-slit spectrathrough peaks or troughs in the plot of the effective radii withwavelength at the wavelength of the spectral feature. However, thesefeatures could only be detected in the decomposition of IFU datacubes if the effective radii of each component were unconstrainedwith wavelength during the fit. However, the S/N of the MaNGAdata is lower than the spectra used by Johnston et al. (2012), inwhich the S/N was ∼53 per Å at the centre of the galaxy, and sothe unconstrained fits produced very noisy results. One possiblesolution would be to perform the decomposition over the spectralregion of interest only (e.g. around a spectral line) and to choose anappropriate polynomial with which to constrain the effective radii.

In addition to creating the smooth decomposed bulge and discdata cubes, it is possible to also create a residuals data cube by

Figure 4. As for Fig. 3 but for the MaNGA broad-band images. It can beseen here that the stacking of the images from the circular fibres smoothesand broadens any features, an effect which is particularly noticeable in theobject on the bottom left of the image. The colour distribution of all imagesis linear, with a range of 99.5 per cent of the total range in pixel values. Thescaling of the residual images has been adjusted to best show any featurespresent.

subtracting the best-fitting model from each image slice. Since theresidual images subtract the smooth model from the non-smoothgalaxy, they can be used to isolate any non-smooth features suchas spiral arms or bright star-forming knots. By stacking the imagesinto a data cube, the spectra of these features can be extracted, thusallowing a separate analysis of their star-formation histories.

3.5 Feasibility in terms of computing power

The four-step process outlined in this section allows the decom-position of a MaNGA data cube to be carried out on a desktop orlaptop computer in a reasonable length of time. For example, usinga Mac laptop with 8GM RAM, the entire decomposition processfrom original data cube to decomposed spectra can be carried outover about ∼9 h for a galaxy using a double Sersic profile over thefull wavelength range of MaNGA. The slowest step of the processis the final fitting of the individual wavelength images, for whichthe time required depends on the complexity of the model used, thenumber of images/wavelength range to be fitted etc. In the exam-ple above, the individual image fits took ∼7.5 h to complete. SinceGALFITM only uses one core at a time for the fits, it is possible to speedup the fitting process for large samples of galaxies by running multi-ple fits simultaneously on powerful computers with multiple parallelcores. Similarly, the fit could be sped up by using the narrow-bandimages to derive the polynomials over the full wavelength range

MNRAS 465, 2317–2341 (2017)




Dow

nloaded from



Figure 5. Decomposed one-dimensional bulge and disc spectra for galaxy 7443-12701 in red and blue, respectively. The black line shows the originalintegrated spectrum, the overplotted purple line is the combined bulge+disc+residual-sky spectra, and the grey line gives the spectrum of the residual-skycomponent. Finally, the green line shows the residuals after subtracting the combined bulge+disc+residual-sky spectra from the original. The top plot showsthe optical spectra, and the bottom plot shows the near-IR spectra with a 500 Å overlap in the wavelength coverage. The feature at 5577 Å in the top plot is the[O I] sky line.

available, but then only applying the fits to individual images overa limited wavelength range to cover only the region of interest forthe analysis.

4 R ELIABILITY TESTS

IFU data generally have smaller fields of view and poorer spatialresolution than imaging data typically used for galaxy fitting. As

a result, the small field-of-view limits the view of the outskirts ofthe galaxy, where the bulge light may dominate the light profileagain, and the poor spatial resolution blurs the signal from the dif-ferent components in the inner regions. In the case of MaNGA,the field of view is limited to show only out to ∼1.5 or 2.5 ef-fective radii, and for all but the most edge-on galaxies there arefew spaxels with no galaxy light with which to quantify Poissonvariations in the residual-sky background, especially around bright

MNRAS 465, 2317–2341 (2017)




Dow

nloaded from



skylines. Therefore, before application to the MaNGA data cubes,the decomposition technique outlined in Section 3 was tested toidentify the reliability of the decomposed spectra and the limita-tions of such analysis. This section outlines a series of tests carriedout to determine the feasibility of fitting galaxies observed withIFU instruments, specifically looking at the effect on the best fitdue to the small field of view and the poorer sampling compared toimaging data.

4.1 Decomposition of simulated galaxies

The largest MaNGA IFU has a field of view of 32.5 arcsec across,and the IFUs are assigned to each galaxy to capture their light outto either 1.5 or 2.5 Re. Since the decomposition of photometricdata with software such as GALFIT and GALFITM generally uses alarger field of view, the first set of tests was designed to identifythe reliability of the decomposition for the various fields of view ofthe MaNGA galaxies. One reliable way of testing such parametersis to create and decompose a series of simulated galaxies in whichthe structural properties and stellar populations are known (see e.g.Simard et al. 2002; Haußler et al. 2007).

The first step in producing these simulated data cubes was tocreate an image of the galaxy with a de Vaucouleurs bulge and ex-ponential disc profile. The images were created with GALFIT using arange of values for the luminosity, effective radius, PA and axes ra-tio for each component. In each model galaxy, the bulge componentwas modelled as the de Vaucouleurs profile with a smaller effectiveradius than the disc, with a total magnitude fainter than the disc byup to 1 mag and with the same PA. Additionally, each image wasconvolved with a PSF image with an FWHM of 2.5 arcsec. A seriesof 96 simulated galaxy data cubes was created, consisting of fourmodel galaxies, each observed at three inclinations (nearly edge-on,intermediate and nearly face-on) with two fields of view (1.5 and2.5 Re) as seen in the four largest MaNGA IFUs (127, 91, 61 and37 fibres).

To create the data cube of the simulated galaxies from theseimages, GALFIT was used to create images of the bulge and disc foreach model. The amount of light in each spaxel from the bulge anddisc was taken to be the fraction of light from each component inthat spaxel. The data cube was then created by coadding the bulgeand disc spectra in the correct proportions for each spaxel.

The bulge and disc spectra were taken from the MILES stel-lar library (Sanchez-Blazquez et al. 2006), which contains stellarspectra of known age and metallicity covering a wavelength rangeof 3525–7500 Å at 2.5 Å (FWHM) spectral resolution (Beifioriet al. 2011; Falcon-Barroso et al. 2011). The ages and metallicitiesof the stellar spectra used to create the simulated galaxies spannedthe ranges of 2 < Age < 15 Gyr and −1.31 < [M/H] < 0.22,respectively. We assigned younger bulges and older discs to twomodel galaxies, and older bulges and younger discs to the othertwo galaxies, where one galaxy for each scenario was assumedto have a single stellar population (SSP) within the bulge anddisc while the other galaxy contained multiple stellar populationswithin each component. Additionally, three of the bulges con-tained higher metallicities than their corresponding discs, whilethe fourth bulge was more metal-poor. For simplicity, it was as-sumed that there were no age or metallicity gradients within eithercomponent. Due to the combination of different stellar populationsselected for each component within each galaxy and the corre-sponding variety of shapes of their spectra, the B/T light ratio var-ied both between each simulated galaxy and with wavelength inthese galaxies.

Finally, a noise component was added to the simulated data cubes.The noise was assumed to be Poissonian and independent of wave-length, and was applied to each image slice within the data cubes.

The simulated data cubes were decomposed as described in Sec-tion 3 using an exponential plus Sersic model. The results for thebulge and disc effective radii and the bulge Sersic indices are givenin Figs 6 and 7, respectively, plotted against the input parameters foreach IFU and field of view. The exception is the bulge Sersic index,which is plotted against model number since the input parametersare the same in each case. The mean uncertainty for each setup isplotted in the bottom right, and represents the statistical uncertain-ties calculated in the fit by GALFITM. It is important to remember thatthe uncertainties calculated by GALFITM are based on a galaxy thatcan be fitted well with the number of components included in themodel and that only has Poissonian noise. Such scenarios are veryrare, and so these uncertainties should be considered a lower limit(Haußler et al. 2007). It can be seen that in the larger IFUs, the fitparameters obtained from the decomposition are relatively close tothe input values, while the smaller IFUs show significantly morescatter. The worst fits were obtained with the 37 fibre IFU, whichhas a field of view of 17 arcsec in diameter. In this case, even withthe simplified models used here, GALFITM struggled to find a goodfit with a two-component model, and the resultant spectra appearedtoo noisy to use.

The increasing scatter in the decomposition parameters towardssmaller IFUs is most likely due to the smaller field of view of theIFUs leading to a smaller number of pixels being used to fit thegalaxy and the residual-sky. Additionally, the 2.5 arcsec FWHMspatial resolution leads to blurring of the bulge and disc light, withthe result that GALFITM is unable to fully disentangle the high andlow Sersic index components in the bulge-plus-disc model used inthis example. These trends however allow us to restrict our sampleselection within MaNGA to those IFUs that provide a sufficientlylarge field of view, and suggests caution when using the decomposedspectra in regions outside of the IFU field of view where the fits arepoorest.

The next step was to determine how much of an effect the scat-ter in the decomposition parameters has on the resultant bulge anddisc spectra and the stellar populations analysis. The results forthe 127, 91 and 61-fibre IFU data cubes can be seen in Figs 8and 9 for the Hβ and [MgFe]′ line strengths, respectively. Theresults for the 37 fibre IFU data cubes are omitted here sincethe fits were so poor that the decomposed spectra appeared toonoisy to be useful. The line strengths were measured using theLick/IDS index definitions, in which the strength of the spec-tral feature is measured relative to a pseudo-continuum calculatedfrom the level of the spectrum in bands on either side (Wortheyet al. 1994; Worthey & Ottaviani 1997). The combined metallicityindex, [MgFe]′, is defined as (Gonzalez 1993; Thomas, Maraston& Bender 2003)

[MgFe]′ =√

Mgb (0.72 × Fe5270 + 0.28 × Fe5335). (1)

The scatter in the line strength measurements is seen to increase fora combination of smaller IFUs and galaxies observed only out to1.5 Re. Additionally, the scatter in the line strengths appears largerfor the discs than for the bulges. This effect is most likely due tothe loss of light from the outskirts of each galaxy due to the smallfield of view of the MaNGA IFUs. The mean uncertainty in theline index measurements can be seen in the bottom right of eachplot, as calculated through a series of numerical simulations withsynthetic error spectra for each galaxy. Since the scatter is generallywithin the error limits, it can be deduced that uncertainties in the

MNRAS 465, 2317–2341 (2017)




Dow

nloaded from



Figure 6. A comparison of the input and output effective radii obtained by GALFITM for a series of simulated data cubes. The top row represents galaxies inwhich 2.5 Re were included in the field of view while the bottom row includes galaxies in which only 1.5 Re are covered, and the columns show the results forthe 127, 91, 61 and 37-fibre IFUs from left to right. The red and blue points represent the bulge and disc components, respectively, while the shape describesthe orientation to the line-of-sight: darker circles are almost face-on galaxies while fainter ovals represent galaxies with higher inclinations.

Figure 7. As for Fig. 6, but showing the results for the Sersic indices of the bulge component. The x-axis in this case is simply the model number since eachsimulated galaxy consisted of an exponential disc and a de Vaucouleurs bulge.

decomposition parameters do not affect the strength of the featuresin the decomposed spectra significantly.

4.2 Comparison with decomposition of SDSS images

The above test assumes that the galaxies being decomposed can bemodelled almost perfectly with a simple two-component model. Inreality however, galaxies have more complicated morphologies dueto the presence of spiral arms, bars, thin and thick discs etc., whichcan affect the fit when the galaxy is modelled as a two-componentsystem. Such additional components may cause further issues whendecomposing IFU data due to the combination of the relatively smallfield of view, poorer spatial resolution and low signal to noise perimage compared to photometric data. A further complication of

the MaNGA data is that the circular fibres and the dither patternused can cause features within the galaxy to become smoothed andslightly broadened once the data are stacked. For example, whilethe expected observational seeing is ∼1.5 arcsec, the FWHM of thereconstructed PSF after fibre sampling and stacking the ditheredimages will be ∼2.5 arcsec (Bundy et al. 2015). However, suchsmoothing may also be useful for the fitting since it removes anysharp, small-scale features that may distort the fit.

To better understand the extent of the limitations when fittingIFU data, both imaging and IFU broad-band images of the galaxiesobserved with the 2014 March and 2015 July commissioning plates(plates 7443 and 7815, respectively) and the 127, 91 and 61-fibreIFUs were decomposed and the results compared. The imaging datawere obtained from the SDSS DR7 (Abazajian et al. 2009) griz-band

MNRAS 465, 2317–2341 (2017)




Dow

nloaded from



Figure 8. As for Fig. 6, but showing the results for the strength of the Hβ absorption features.

Figure 9. As for Fig. 6, but showing the results for the strength of the combined [MgFe] absorption features.

images, and mosaicked together with the MONTAGE software3 to pro-duce a large field of view (∼8 arcmin centred on the galaxy) for thetwo-dimensional image decomposition. The MaNGA broad-bandgriz images and corresponding PSF files are provided as part ofthe MaNGA data products included with each data cube. Thesebroad-band images were created by using the griz-band transmis-sion curves to stack the relevant images in the data cube in the rightratios, and thus are a useful comparison to the imaging data.

The imaging and IFU images for each galaxy were fitted in thesame way using the same starting parameters, and all fits started witha single exponential profile to represent the disc plus a residual-skybackground component. In all cases, the residual-sky backgroundwas assumed to be constant over the field of view in each image.After each fit, the residual images, which were generated by GALFITM

by subtracting the best-fitting model from the original image, were

3 http://montage.ipac.caltech.edu/

checked by eye to identify whether the addition of another com-ponent in the inner regions would improve the fit. In cases wherethe residual images showed obvious over/undersubtraction of thegalaxy light in the inner regions, or where dark rings/patches couldbe seen, the fits were repeated with an additional Sersic or a PSFprofile to identify which combination produced the best fit. Theresidual images were again checked by eye and compared to theearlier fit to determine whether an improvement had been achieved.While comparing the residual images by eye is not guaranteed todetermine whether the best fit has been achieved, for a small sampleof galaxies it is a useful indicator as to whether one or two com-ponents provide the best fit. Similarly, the residual images can helpidentify whether GALFITM has settled on a local minimum, resultingin a poor overall fit. By checking the fits by eye in this way, itwas found that good fits for the MaNGA broad-band griz imagesfrom the 61-fibre IFU could only be achieved when using a singlecomponent. As described in Section 4.1, the small number of spax-els in these images contributes to the poorer fits when additional

MNRAS 465, 2317–2341 (2017)




Dow

nloaded from

http://montage.ipac.caltech.edu/



components were added. Additionally, due to the IFU selection forMaNGA galaxies to cover out to at least 1.5 effective radii, thegalaxies observed with the 61-fibre and smaller IFUs are smallergalaxies in general, leading to increased blurring of the light fromeach component at smaller radii.

For each component, the effective radius and Sersic index (whereapplicable) were constrained to a linear polynomial over the fourwavebands, the axes ratio and PA were constrained to remain con-stant with waveband, and the magnitudes were allowed completefreedom. Fig. 2 presents an example of the results for the decompo-sition parameters of 7443-9102 from the imaging data over plottedon the results from the decomposition of the narrow-band imagesdescribed in Section 3. Despite the difference in the S/N of thebroad-band and narrow-band images, the fit parameters are verysimilar over the wavelength range. The main difference lies in theSersic index of the bulge, which is likely to be due to the varied lev-els of blurring by the different spatial resolutions of the photometricand spectroscopic data, as described in Section 3.3.

Fig. 10 presents each galaxy that was analysed, along with theIFU field of view and whether it was successfully fitted with theexponential or exponential-plus-Sersic profile. Of the 22 galaxiesanalysed in this way, 13 galaxies were successfully fitted in bothdata sets, indicating a success rate of ∼59 per cent. Reasons for theunsuccessful fits include galaxies that were not simple disc-onlyor bulge-plus-disc systems, including one case where the IFU wascentred on two interacting galaxies, or where the galaxies were tooface-on and the residual-sky background could not be fitted reliably,especially where the spatial coverage extended out to only 1.5 Re

of the galaxy.A comparison of the bulge and disc fit parameters obtained for

the imaging and MaNGA broad-band images is given in Fig. 11,where the different colours and symbols correspond to the differentwavebands for each galaxy that could be successfully modelled.The mean statistical uncertainty for each parameter over all fourbands as calculated by GALFITM is plotted in the bottom right of eachplot. It can be seen that the effective radius of the disc appears ingeneral overestimated slightly in the MaNGA data relative to theimaging data, particularly in the case of a fixed exponential disc.The effective radii of the bulges of two galaxies in the MaNGAdata were also measured to be larger than in the imaging data bya factor of more than 3. At this point, it is important to rememberthat the hexagonal MaNGA field of view is smaller than the squareimage size, and so the regions outside of the MaNGA field of vieware masked out when a fit is applied with GALFITM. However, as canbe seen in the model and residual images of Fig. 4, the best-fittingmodel created by GALFITM expands into the masked region. Thus,GALFITM creates a best-fitting model for the whole galaxy despiteonly having information on the inner regions. To check the effecton the fits with the outer regions masked out, the fits carried outin this section were repeated using the SDSS images with a maskrestricting the field of view to that seen by the MaNGA data. Thedecomposition parameters were then compared to those obtainedwith the full field, and the same trends as shown in Fig. 11 wereobtained. Therefore, it is believed that the overestimation in theeffective radii of the two components in Fig. 11 is likely to bedue to this loss of light from the outer, disc-dominated regions ofthe galaxy and the subsequent less-accurate fits to these regions byGALFITM.

Since not all galaxies have perfectly exponential discs (van derKruit 1979; Pohlen et al. 2002; Maltby et al. 2012), these fits wererepeated starting with a single Sersic profile instead of the expo-nential profile. With this model, 15 galaxies could be decomposedsuccessfully, increasing the success rate to ∼68 per cent. The re-

sults given in Fig. 11 appear to show a better correlation between thetwo data sets. The Sersic indices for the discs now show the largestscatter, again most likely due to the loss of light in the outermost re-gions affecting the fits, but given the small values of the disc Sersicindices, the variation is not so large. The disc effective radii showa smaller overestimation than when the discs were constrained toexponential profiles, and the scatter in the bulge sizes and Sersicindices is also lower in amplitude. Combined, these trends indicatethat in some galaxies, better fits can be obtained for the MaNGAdata when their discs are modelled as Sersic profiles as opposed toexponential profiles.

Since the IFU and imaging data have similar spatial resolutions,2.5 and 1.3 arcsec FWHM of the PSF, respectively, the scatter in theplots in Fig. 11 should not be significantly affected by the differentresolutions. Instead, it is most likely attributed to the smoothingcreated by stacking the circular apertures of the fibres, and theloss of light in the outskirts of each galaxy leading to the poorfitting of the bulge and disc light in these regions. Examples ofa double-Sersic decomposition for 7815-9102 for the SDSS andMaNGA broad-band images are shown in Figs 3 and 4, respectively,giving the griz broad-band images along with the correspondingbest-fitting models and the residual images. These images showthat the features in the MaNGA data are smoother and broaderwith less pixel-to-pixel variations than the SDSS images due tothe correlated signal and noise among spaxels compared to themore independent SDSS image pixels. This smoothing is primarilydue to the PSF covering five pixels in the MaNGA images, whilein the SDSS images the PSF covers only three pixels. Addition-ally, the residual images for the MaNGA data show how the bestfit to the galaxy extends beyond the MaNGA field of view, leadingto the poor separation of bulge and disc light at large radii. However,despite these differences between the data sets, the decompositionparameters measured from the imaging and MaNGA data for thisgalaxy were found to be consistent.

4.3 GALFITM versus GALFIT

One of the key strengths of GALFITM over GALFIT is that by fittingmultiple images simultaneously, the S/N of the entire data set in-creases over that of any individual image. Additionally, by fittingthe decomposition parameters as polynomials as opposed to dis-crete values, a reasonable estimate of the parameters of individualimages with low S/N can still be obtained.

To appreciate how much of an improvement is achieved in thefits using GALFITM, the decompositions described in Section 4.2 wererepeated using GALFITM with all parameters allowed complete free-dom to emulate the results GALFIT would give. The results are givenin Figs 12 and 13 for the decompositions starting with exponentialand Sersic profiles, respectively, for both the MaNGA and SDSSdata sets.

While carrying out the free fits, it was immediately clear thatwithout any constraints from the other multiwaveband images ofthe same galaxy, GALFITM was finding very unphysical parametersfor some images. For example, some galaxies were fitted with Sersicindices of between 10 and 20, axes ratios of less than 0.1 or effectiveradii of less than half a pixel. Such poor fits consequently make upthe majority of the outliers in Figs 12 and 13 and emphasize thestrength of using GALFITM to decompose images from data cubesreliably.

The amplitudes of the scatter in the results for Re and n are re-duced when the disc is constrained to an exponential profile, thoughsome outliers due to poor fits are still present. However, as was dis-cussed in Section 4.2, not all of the galaxy discs are best represented

MNRAS 465, 2317–2341 (2017)




Dow

nloaded from



Figure 10. SDSS images of the galaxies observed with the 127, 91 and 61 fibre IFUs on commissioning plates 7443 (left) and 7815 (right). The platenumber-IFU number is listed at the top right of each galaxy, and the field of view of the IFU is over plotted. The ticks and crosses in the bottom right of eachimage show whether or not that galaxy could be fitted with either an exponential or an exponential-plus-Sersic profile, and the crosses with asterisks show thetwo galaxies in which fits could only be obtained when a Sersic profile was used to model the disc instead of an exponential profile.

MNRAS 465, 2317–2341 (2017)




Dow

nloaded from



Figure 11. Comparison of decomposition parameters for SDSS and MaNGA broad-band images where the decompositions assume an exponential (left) andSersic (right) disc. From top to bottom are the effective radii for the bulge and disc, then the Sersic indices for the bulge and disc. The griz-band images arerepresented as green squares, red circles, yellow upward-pointing triangles and grey downward-pointing triangles, respectively. In all cases, galaxies were fittedwith an exponential disc with either an additional Sersic or PSF profile added where this additional component was found to improve the fit. The colours referto the band that each measurement corresponds to.

by an exponential profile and by forcing this one constraint, thesize of the disc and the model for the bulge may also be affected.

4.4 Summary

Together, the results presented in this section show that the largenumber of images in an IFU data cube that can be decomposed si-multaneously leads to a better extraction of information, even withsmall fields of view and poor spatial resolution. Therefore, if the de-composition of an IFU data cube is carried out carefully and initiatedwith reasonable staring parameters, reliable results for the indepen-dent stellar populations within each component can be obtained.

5 E X A M P L E A NA LY S I S O F T H EDE COMPOSED SPECTRA

Traditional stellar population analysis of galaxies using spectra typi-cally involves using radially binned spectra, where each bin contains

a superposition of light from each component. The spectroscopic de-composition technique outlined above produces decomposed spec-tra representing purely the light from each component, thus reducingthe contamination from other light sources and allowing us to studytheir individual star formation histories.

In this section, we present example stellar population analysesfor the separated bulge and disc spectra from galaxies 7443-12701and 7443-9102 in order to demonstrate the potential of the methoddescribed in this paper. These two galaxies were selected since theyare both early-type disc galaxies with no strong emission featuresor other significant structures such as spiral arms, and could bedecomposed with a bulge-plus-disc model. Images of the galaxies,along with the field of view of the IFUs, are shown in Fig. 10. Bothgalaxies were observed as part of the Primary MaNGA sample,meaning that they were observed out to ∼1.5 effective radii asmeasured from single Sersic fits.

7443-12701 has been classified as having a probability of 0.57and 0.75 of being an early-type galaxy by Huertas-Company et al.

MNRAS 465, 2317–2341 (2017)




Dow

nloaded from



Figure 12. Comparison of decomposition parameters for SDSS and MaNGA griz broad-band images (right and left, respectively) obtained using GALFITM

for constrained fits and GALFIT for completely free fits. The plots from top to bottom represent the bulge and disc effective radii and the bulge and disc Sersicindices. In all cases, galaxies were fitted with an exponential disc with either an additional Sersic or PSF profile added where this additional component wasfound to improve the fit.

(2011) and Lintott et al. (2011), respectively, and the single-fibreSDSS DR-12 data for this galaxy show features indicative of apost-starburst spectrum. It lies at a redshift of z ∼ 0.020 (Aiharaet al. 2011) and was observed with a 127-fibre IFU with a field ofview of 32.5 arcsec in diameter. Fig. 10 shows that the galaxy wasoffset from the centre of the IFU, the purpose of which was to test theastrometric routines using the nearby star during commissioning.This offset is unusual within the MaNGA pointings, but provideda useful first test for our decomposition since the model could befitted to the outskirts of the disc and the sky on one side. A faint barcan also be seen in this galaxy, and the effect on the fit is discussedin Section 3.

The second galaxy, 7443-9102, has been classified as anearly-type galaxy with probabilities of 0.90 (Huertas-Companyet al. 2011) and 0.79 (Lintott et al. 2011). It lies at a redshift ofz ∼ 0.092 (Aihara et al. 2011), and was observed with the 91-fibre

IFU with a field of view of 27.5 arcsec. This galaxy is a typical ex-ample of an observation of a Primary sample galaxy within MaNGAsince it is centred within the IFU.

Both galaxies were decomposed as described in Section 3, andlight- and mass-weighted stellar populations analyses were carriedout on the decomposed one-dimensional bulge and disc spectra.

5.1 Light-weighted stellar populations

The light-weighted stellar populations of the decomposed spectrawere measured using the hydrogen, magnesium and iron absorption-line strengths as indicators of age and metallicity, respectively. Theline strengths were measured using the Lick/IDS index definitions,and the combined metallicity index, [MgFe]′ (see equation 1), wasused due to its negligible dependence on the α-element abundance(Gonzalez 1993; Thomas et al. 2003). The age was measured using

MNRAS 465, 2317–2341 (2017)




Dow

nloaded from



Figure 13. As for Fig. 12 but for the fits that assumed a Sersic profile for the disc.

the Hβ absorption feature, corrected for contamination from emis-sion by using the [OIII]λ5007 emission line strength in the relation(Trager et al. 2000)

�(H β) = 0.6 × EW[O III]λ5007, (2)

where the equivalent width of the [O III]λ5007 feature was measuredfrom the residual spectrum obtained by subtracting the best com-binations of stellar templates produced by PPXF from the originaldecomposed spectrum. The uncertainties in the line index measure-ments were estimated from the propagation of random errors andthe effect of uncertainties in the line-of-sight velocities.

The SSP models of Vazdekis et al. (2010) were used to convertthe line index measurements into estimates of the relative light-weighted ages and metallicities. These SSP models were createdusing the MILES stellar library, in which the spectra have a spectralresolution of 2.5 Å (FWHM) and are convolved with a Gaussianof the appropriate dispersion to reproduce the spectral resolution

of the data using a web-based tool.4 The resultant SSP models arethus matched to the data, minimizing the loss of information thatnormally occurs when degrading the data to match lower resolutionmodels.

An example of the one-dimensional decomposed bulge and discspectra for galaxy 7443-12701 and the original integrated spectrumare shown in Fig. 5. These spectra were obtained by fitting Sersicprofiles to both components and identifying the bulge as the centralcomponent with the higher Sersic index and smaller effective radius.To further improve the fit to the image, the red star at the top of theMaNGA field of view of that galaxy (see Fig. 10) was also includedin the fit using a PSF profile to model a point source. Similarly,for 7443-9102, an additional Sersic profile was added to the fit tomodel the bright structure to the upper left of the galaxy.

The left-hand panels of Fig. 14 show the line index measure-ments for bulge and disc components of each galaxy plotted over

4 http://miles.iac.es/

MNRAS 465, 2317–2341 (2017)




Dow

nloaded from

http://miles.iac.es/



Figure 14. Index–index diagram for galaxies 7443-12701 (top) and 7443-9102 (bottom) using the indices Hβ versus [MgFe]′, with SSP model predictionsof Vazdekis et al. (2010) overplotted. From left to right are the line index measurements from the decomposed integrated bulge and disc spectra, the radiallybinned MaNGA data cube after obliterating the kinematics but before the decomposition, and the radially binned bulge-plus-disc data cube obtained from thedecomposition. The hollow symbols in the left plot represent the line strengths measured from the best-fitting spectra obtained from the regularized PPXF fits.The data points in the middle and right plots are colour-coded according to radius from the centre of the galaxy.

the corresponding SSP model. The errors shown represent the sta-tistical uncertainties in the line index measurements as estimatedfrom the effect of uncertainties on the line-of-sight velocities. Theglobal, luminosity-weighted ages and metallicities of the bulge anddisc are calculated by interpolating across the SSP model grid. In7443-12701, the bulge appears to contain younger and more metal-rich stellar populations than the disc. Since these models only giveestimates of the light-weighted ages of each component, these agesshould not be taken as a representation of the age of the component,but more as an indication of how long ago the final episode of starformation occurred and thus when the gas was stripped out or usedup. In this galaxy, the light-weighted stellar populations suggestthat the final episode of star formation occurred in the bulge region.Such a result is at first surprising since this galaxy appears to be anearly-type disc galaxy with no obvious spiral arms or strong emis-sion features. However, similar trends have been noted recently inS0 galaxies. For example, Johnston et al. (2012, 2014) decomposedlong-slit spectra of S0 galaxies in the Virgo and Fornax clustersand found evidence that the final episode of star formation in these

galaxies occurred within their bulge regions. Further evidence ofrecent star formation in bulge regions of S0s has been detected byPoggianti et al. (2001), Ferrarese et al. (2006), Sil’Chenko (2006),Kuntschner et al. (2006) and Thomas & Davies (2006), and a studyby Rodrıguez Del Pino et al. (2014) found evidence that the mostrecent star formation activity in discy cluster ‘k+a’ galaxies, whichare thought to be a transitional phase between spirals and S0s, wascentrally concentrated within the disc.

To check the reliability of these results, the stellar populationsof the two components were compared to those from across thewhole galaxy before decomposition. The kinematically obliterateddata cube, obtained as an intermediate product of the decompositionoutlined in Section 3.1, was radially binned using the Voronoi bin-ning technique of Cappellari & Copin (2003), and the line indicesof the binned spectra measured in the same way as the decomposedspectra. The kinematically obliterated data cube was selected forthis analysis since it produces a uniform set of binned spectra withminimal variation in the line-of-sight velocities and velocity dis-persions over the galaxy, and thus allows the line strengths to be

MNRAS 465, 2317–2341 (2017)




Dow

nloaded from



overplotted on the same SSP model. These results are plotted inthe top-middle SSP model of Fig. 14, colour-coded according toradius after correcting for the inclination of the galaxy, and showthe same trend of increasing age and decreasing metallicity withradius, albeit with more measurement noise.

As a final comparison, this process was repeated for the decom-posed bulge-plus-disc data cube. Again, the results are plotted onthe top right of Fig. 14, showing the same trend as the Voronoi-binned data cube but with reduced noise due to the smoothing inthe stellar populations by the fitting process.

It is important to remember that 7443-12701 is not a typical ex-ample of a MaNGA galaxy since it is offset from the centre of thefield of view. 7443-9102 is a more typical example of a MaNGAobservation for a galaxy in the Primary sample, and the same stellarpopulations analysis are presented in the lower panels of Fig. 14.Even with the smaller field of view that cuts off the light from theoutskirts of the galaxy, a good fit was achieved. The SSP modelresults for the radially binned data cube before decomposition showa larger scatter than 7443-12701, particularly outside of 3 arcsec,which is most likely attributable to the smaller differences in theline strengths for older stellar populations. However, the estimatesfor the global light-weighted bulge and disc stellar populations(bottom-left panel of Fig. 14) are consistent with those the radi-ally binned data cube before decomposition (bottom-middle panel).These consistent results provide a further indication that the decom-position technique presented in this paper can be applied to IFU datasuccessfully, even when only the inner 1.5 Re of the galaxy can beobserved.

As with 7443-12701, this galaxy is also likely to be an S0 galaxy,but the stellar populations show a very different trend. Due to thesmall differences in the Hβ line strengths in older stellar popu-lations, it can be assumed that the bulge and disc contain stellarpopulations of approximately similar ages. The decomposed bulgespectrum however shows a higher average metallicity than the discspectrum. The older ages suggest that it is likely that this galaxy un-derwent the transformation into an S0 longer ago than 7443-12701,however the small differences in the Hβ line strengths at suchages make it difficult to determine reliable age gradients across thisgalaxy. The metallicity gradient on the other hand suggests that thegas that fuelled the most recent star formation within the inner re-gions of the galaxy was more metal enriched than the gas fuellingthe latest star formation in the outer regions. Since bars are thoughtto drive gas through the disc into the inner regions of a galaxy(Kormendy & Kennicutt 2004), it is possible that this metallicitygradient was produced by a bar that existed before the star forma-tion ceased. Flat age gradients between the bulge and disc regionsof S0s have also been found within the CALIFA survey GonzalezDelgado et al. (2015), while Rawle et al. (2008) have also detectedflat age and negative metallicity gradients across early type galaxiesin Abell ∼3389.

While the light-weighted ages and metallicities of the bulgesand discs mainly tell us roughly how long ago the last episode ofstar formation was truncated, the magnesium-to-iron abundancescan provide information on the star formation time-scales of eachcomponent. The magnesium and iron line strengths were measured,with the iron index calculated as

〈Fe〉 = (Fe5270 + Fe5335)/2. (3)

The results can be seen in Fig. 15 for the decomposed, one-dimensional bulge and disc spectra, the radially binned data cubeafter obliterating the kinematics, and the radially binned bulge+discdata cube. The stellar population models of Thomas et al. (2011) are

overplotted for α/Fe ratios of 0.0, 0.3 and 0.5, metallicities rangingbetween −1.35 and +0.67, and ages of 2 and 12 Gyr, where theseages were taken as the approximate mean ages of 7443-12701 and7443-9102, respectively, from Fig. 14.

The metallicity gradient between the bulge and disc in 7443-9102can again be clearly seen in Fig. 15. Both galaxies show supersolarα/Fe ratios, with the bulge and disc values in each galaxy runningapproximately parallel to the lines of constant α/Fe. This trendsuggests that both components underwent similar star formationtime-scales. A similar result was found by Johnston et al. (2014)in their decomposed long-slit spectra of Virgo cluster S0s, and it isinteresting to see the same trend appear in these two very differentearly-type disc galaxies. Together, these results suggest that bulgeand disc formation may be tightly coupled in such galaxies, and itwould be interesting to see if this conclusion remains intact with alarger sample.

The plots in Figs 14 and 15 clearly show that both the one-dimensional decomposed spectra and the two-dimensional datacube for each component form an accurate representation of theglobal light-weighted stellar populations of the different structuralcomponents.

5.2 Mass-weighted stellar populations

The light-weighted stellar populations measured within a galaxycan easily be affected by small amounts of recent star formation,leading to the measurements being biased towards younger ages.Therefore, while these measurements are useful for determininghow long ago the most recent star-formation activity occurred, theyprovide little information as to the star formation history over thelifetime of the galaxy.

To get a better idea of the star formation histories of the decom-posed components, the mass-weighted ages and metallicities caninstead be used. The mass-weighted ages and metallicities for eachdecomposed bulge and disc spectrum were calculated using thePPXF code to fit a linear combination of template spectra of knownrelative ages and metallicities. The MILES spectra described inSection 4.1 were used in these fits, with 300 spectra covering aregularly sampled grid with ages in the range 0.06–18 Gyr andmetallicity spanning [M/H]= −1.71 to +0.22. To reduce the de-generacy between the ages and metallicities of the binned spectra,linear regularization (Press et al. 1992) was used to smooth thevariation in the weights of neighbouring template spectra within theage–metallicity grid. The degree of smoothness in the final solutionand the quality of the final fit to the galaxy spectrum were controlledwithin PPXF via the regularization parameter. While this smoothingmay not completely reflect the true star formation history of thegalaxy, which is likely to be stochastic and variable over short time-scales, the smoothing does reduce the age–metallicity degeneracyfrom bin to bin when applied to binned spectra from across a galaxy,thus allowing a more consistent comparison of systematic trends inthe star formation history over the whole galaxy.

The first step to measuring the mass-weighted stellar populationswas to apply an unregularized fit to the bulge and disc spectra and tomeasure the χ2 value. Using this fit as the control fit, the spectrumwas re-fit with a range of values for the regularization parameteruntil the χ2 value increased by an amount equal to

√2N , where

N is the number of pixels in the spectrum being fit. This criterionidentifies the boundary between a smooth fit that still reflects theoriginal spectrum, and a fit that has been smoothed too much andno longer represents the star formation history of the galaxy.

MNRAS 465, 2317–2341 (2017)




Dow

nloaded from



Figure 15. Index–index diagram for galaxies 7443-12701(top) and 7443-9102 (bottom) using the indices Mgb versus 〈Fe〉, with model predictions of Thomas,Maraston & Johansson (2011) overplotted. The models used for 7443-12701 and 7443-9102 are for ages of 2 and 12 Gyr, respectively, where these values arethe approximate mean ages of these galaxies from Fig. 14. As in Fig. 14, the plots from left to right show the line index measurements from the decomposedintegrated bulge and disc spectra, the radially binned MaNGA data cube after obliterating the kinematics but before the decomposition, and the radially binnedbulge-plus-disc data cube obtained from the decomposition. The hollow symbols in the left plot represent the line strengths measured from the best-fittingspectra obtained from the regularized PPXF fits. The data points in the middle and right plots are colour-coded according to radius from the centre of the galaxy.

The template spectra are modelled for an initial birth cloud massof one solar mass, and so the final weight of each template reflectsthe ‘zero-age’ mass-to-light ratio of that stellar population. There-fore, the smoothed variation in the weights of neighbouring tem-plate spectra in the final regularized fit represents a simplified starformation history of that part of the galaxy by defining the relativemass contribution of each stellar population (see e.g. McDermidet al. 2015). The mean mass-weighted ages and metallicities of thebulge and disc of these two galaxies were calculated using

log(AgeM-W) =∑

ωi log(Agetemplate,i)∑ωi

(4)

and

[M/H]M-W =∑

ωi[M/H]template,i∑ωi

, (5)

respectively, where ωi represents the weight of the ith template (i.e.the value by which the ith template stellar template is multipliedto best fit the galaxy spectrum), and [M/H]template, i and Agetemplate, i

are the metallicity and age of the ith template, respectively. Theresults for decomposed bulges and discs of galaxies 7443-12701and 7443-9102 are shown in Fig. 16, along with error bars esti-mated by Monte Carlo simulations of model galaxies constructedusing the same components as in the best fit to each spectrum.These values are plotted at the effective radius of that componentas measured from the two-component fit to the galaxy at 4770 Åwithin the data cube. This wavelength is the central wavelengthof the g band, whose bandwidth covers the Hβ, magnesium andiron lines used in Section 5.1. Although the estimates for the light-and mass-weighted stellar populations of each component are dif-ferent, the same trends can be seen. 7443-12701 for example stillshows the younger and more metal-rich bulge compared to its disc,while in 7443-9102 the bulge and disc ages are similar while the

MNRAS 465, 2317–2341 (2017)




Dow

nloaded from



Figure 16. Top: the normalized flux for the radially binned spectra in galaxy 7443-12701 (left) and 7443-9102 (right) against radius from the centre of thegalaxy after correction for inclination. The light profile of the bulge (red dashed line) and disc (blue dot–dashed line) are overplotted, as calculated from thedecomposition parameters at 4770 Å and convolved with a PSF of FWHM 2.5 Å. The black solid line shows the bulge+disc light profile, the horizontal linegives the level of the residual-sky background from the fit, and the vertical dashed line shows the effective radius of the galaxy when fitted with a single Sersicprofile (Simard et al. 2011). Upper middle: the B/T (red dashed line) and D/T (blue dot–dashed line) light ratios as a function of radius. Lower-middle andbottom: the mass-weighted ages (upper) and metallicities (lower) for the bulge and disc (red circle and blue ellipse, respectively), plotted against the effectiveradius of that component as measured from the two-component fit to the galaxy at 4770 Å. The radially binned measurements are shown as the grey pointswith their associated errors, and the solid line represents the averaged, radially binned mass-weighted ages and metallicities. The dashed line represents theerrors added in quadrature for each averaged measurement.

bulge shows higher metallicity than the disc. As a further checkon the reliability of these results, the line strengths of the best fitto each decomposed spectrum were measured and compared withthose of the decomposed spectra. The line strengths were found tobe consistent between the decomposed and best-fitting spectra, ascan be seen in Figs 14 and 15.

As in Fig. 14, the mass-weighted ages and metallicities of theVoronoi-binned spectra are also plotted against the radius of eachbin, having been measured in the same way. The radially averagedmass-weighted ages and metallicities are overplotted as the solidline, and the uncertainty in this trend marked as the dashed lines asmeasured by adding in quadrature the errors on the measurementsused in the radial binning. In both cases, the radial trend followsthe trend between the bulge and disc, indicating that no significantinformation was lost from the bulge and disc spectra as a result of the

decomposition process. The scatter is simply due to the variationsin the stellar populations over the galaxy.

For comparison, Fig. 16 also shows the light profile of eachgalaxy, as measured from the broad-band image covering the centreof the g band (4770 Å), along with the Sersic profiles for the bulgeand disc and the bulge-plus-disc profile at that wavelength. Theseprofiles have been convolved with the appropriate PSF to reflect thespatial resolution of the final data cube. The level of the residual-sky background, as measured by GALFITM, and the effective radiusmeasured from a single Sersic fit (g band; Simard et al. 2011) arealso plotted at the horizontal and vertical dotted lines as a reference.This plot, combined with the plot for the variation in the B/T anddisc-to-total (D/T) light ratios with radius, indicates the proportionof bulge and disc light at each radius in the SSP models, and thusthe radius at which the disc dominates the light of the galaxy.

MNRAS 465, 2317–2341 (2017)




Dow

nloaded from



Figure 17. The star-formation histories of the bulges (red) and discs (blue)of galaxies 7443-12701 (top) and 7443-9102 (bottom). The star formationhistory is defined as the relative fraction of stellar mass created as a functionof the lookback time, and was derived from the regularized fit to the bulgeand disc spectra with MILES template spectra. The shaded region aroundeach line shows the rolling standard error on the mean value at each lookbacktime, as estimated from the standard deviation in the mass fractions in eachage bin divided by the square root of the number of measurements used inthe bin.

The regularized weight of each template from PPXF reflects therelative mass contribution of that stellar population, and thereforethe mass created at that time. Using these weights, the estimatedstar-formation histories of the bulges and discs of galaxies 7443-12701 and 7443-9102 were derived, and are shown in Fig. 17.The star formation histories are plotted as the mass fraction of eachcomponent created as a function of time, where the smooth variationis a result of the regularization outlined above. The standard errorson the mass fractions are marked as the shaded regions, estimatedfrom the standard deviation in the mass fractions in each rolling-agebin divided by the square root of the number of measurements usedin the bin. In 7443-9102, the star formation in the bulge and discceased a long time ago, reflecting the results from the light-weightedstellar populations analysis. 7443-12701 on the other hand showsmore recent and extended star formation in both components. Withinthe disc, the star formation has slowly truncated since ∼8 Gyr ago,whereas two star formation events can be seen in the bulge at ∼5and ∼1 Gyr ago. This recent episode of star formation in the bulgedominates the luminosity of the bulge, and thus biases the light-weighted age of the bulge to younger values.

5.3 Decomposition and analysis of simulated data cubes

The example analyses presented above show promising results thatthe decomposed bulge and disc spectra reliably reflect the stellarpopulations and star-formation histories of those components. How-ever, as a final test of the reliability of the technique presented inthis paper, the decomposition and analysis were repeated for a seriesof simulated galaxies created using the decomposed bulge and discspectra of 7443-12701 and 7443-9102.

For each galaxy, 10 simulated galaxy data cubes were created bycombining two data cubes representing the galaxy and the back-ground noise. The galaxy data cube was created by adding togetherthe decomposed bulge and disc data cubes with the residual-skybackground. To achieve a realistic test, a sensible amount of noise

Figure 18. A comparison of image slices from the original (left) and sim-ulated (right) data cubes for 7443-12701 and 7443-9102 (top and bottom,respectively) at 4990 Å. The images have been scaled logarithmically onthe same flux scale, which has been adjusted to maximally display thesmall-scale variations in the background.

must be added to this data cube, which could technically be doneby simply adding Poisson noise to each pixel in this cube. However,as MaNGA data cubes are created by combining dithered pointingswith each fibre-IFU, the level of the noise in neighbouring spaxelsis correlated in those data cubes, and therefore must be re-createdin the simulated noise. An example of this effect can be seen in theimages on the left side of Fig. 18, in which the flux scales have beenadjusted to display the small-scale variations in the backgroundnoise. This noise correlation must be reflected in the noise addedfor this simulated data cube. To achieve this effect, the noise datacubes – before adding them on to the noise-less data cube – wereconvolved with a PSF profile of varying FWHM until the structureof the noise resembled that within the MaNGA cubes. Finally, thesimulated galaxy data cubes were combined with the noise datacubes and compared by eye to the original data cubes at the samewavelength. When using the Poissonian noise levels alone as thestarting point for the noise data cube, due to the smoothing the finalsimulated data cube was found to have too low levels of backgroundvariations when compared to the original data cube at the same fluxlevel. Instead, the closest similarity was achieved when the Poissonnoise was multiplied by a factor of 5 and convolved with a PSF of3 pixels FWHM for both galaxies. Fig. 18 gives a comparison ofthe original and simulated data cubes at 4990 Å on the same fluxscales.

The simulated data cubes were decomposed in the same wayas the original MaNGA data cubes, and the analysis described inSections 5.1 and 5.2 applied to the decomposed spectra. At thispoint, it is important to note that, because we do not smooth the noisein the simulated data cubes in the spectral direction, the decomposedsimulated spectra contain higher levels of noise than the originaldecomposed spectra since they additionally include the noise thatwas already present in the decomposed bulge and disc data cubes.The analysis here hence presents a worst-case scenario, which likelyoverpredicts the error bars of our analysis.

MNRAS 465, 2317–2341 (2017)




Dow

nloaded from



Figure 19. Index–index diagrams for the decomposed bulge and disc spec-tra from each simulated galaxy based on 7443-12701 (left) and 7443-9102(right). As in Figs 14 and 15, the models overplotted in the top row are thoseof Vazdekis et al. (2010), and the models of Thomas et al. (2011) are usedin the bottom row. The hollow black circle and ellipse represent the resultsfor the decomposed bulge and disc spectra, respectively, from the originaldata cube. The mean uncertainties for each plot are shown in the top rightor top left of each plot.

The light-weighted stellar populations analysis for each simu-lated galaxy is shown in Fig. 19, and appears consistent with thosein Figs 14 and 15 (as shown by the hollow symbols). The largeruncertainties and the scatter in the simulated galaxy results werefound to simply reflect the higher noise levels in those data cubes,which resulted in noisier decomposed spectra. The largest discrep-ancy between the real and simulated results is in the values forthe line indices measured in the decomposed discs of the simu-lated galaxies based on 7443-9102, which is most noticeable in thebottom-right plot of Fig. 19. While the results from 6 of the 10 sim-ulated discs agree very well with each other and lie within the errorbars of the original decomposed disc measurements, the remainingfour measurements show larger scatter. When looking at the lineindex measurements across the decomposed bulges and discs ofeach simulation, it was found that if one component overestimatedthe line strength, the other underestimated it proportionally. Thiseffect likely arose from the lower S/N in the simulations in compar-ison to the original data cubes, which led to larger variation in themagnitudes of the fits. Since the decomposed bulge and disc spec-tra of galaxy 7443-9102 appear noisier than those of 7443-12701,and consequently the corresponding simulations also contain higherlevels of noise, this effect is stronger in this case. Furthermore, itappears strongest in the Mgb index, potentially because it formspart of a triplet which is blurred together in the first step of thedecomposition process outlined in Section 3.

The mass-weighted stellar populations for the simulated galaxiesare presented in Fig. 20, overplotted with the results from the radi-ally binned and decomposed spectra from Fig. 16 as a comparison.

Figure 20. The mass-weighted ages (upper) and metallicities (lower) for thebulges and discs (red circle and blue ellipse, respectively) of the simulatedgalaxies, plotted against the effective radius of that component as measuredfrom the two-component fit to the galaxy at 4770 Å. As in Fig. 16, the radiallybinned measurements from the original data cubes are shown as the greypoints with their associated errors, along with the averaged, radially binnedmass-weighted ages and metallicities and the errors added in quadraturefor each averaged measurement. Red: as a reference, the black circles andellipses represent the results for the decomposed bulge and disc spectra,respectively, from the original data cube, red; as shown in Fig. 15. The meanuncertainties in the simulated bulge and disc measurements are shown inthe bottom-right corner of each plot.

Each age and metallicity measurement is plotted at the effectiveradius of that component, as measured during the decompositionof that simulated galaxy. Again, the results appear largely consis-tent with those obtained from the original galaxies, with the mainexception being the ages of the simulated discs in 7443-9102. Thisdiscrepancy may be due to the higher levels of noise in the decom-posed spectra as well as the small variations in the line strengths atsuch high ages. It is interesting to note that the effective radius ofthe bulge of the simulated galaxies based on 7443-9102 also showsa large variation. The original fit for this galaxy contained a high-Sersic index bulge, which consequently was used in the simulatedgalaxies. It is likely that the variation in the measured effective radiiof the bulges of the simulated galaxies is simply due to the combi-nation of the high Sersic index, small size and elevated noise levelsin the simulated galaxies. However, despite the variation in theirsizes, the mass-weighted ages and metallicities appear consistentacross the 10 simulated galaxies. This result is consistent with the

MNRAS 465, 2317–2341 (2017)




Dow

nloaded from



Figure 21. The star formation histories of the bulges (red) and discs (blue)of the simulated galaxies based on 7443-12701 (top) and 7443-9102 (bot-tom). The star formation history is defined as the relative fraction of stellarmass created as a function of the lookback time, and was derived from theregularized fit to the bulge and disc spectra with MILES template spectra.

finding of Johnston et al. (2014), who found that the stellar popula-tions derived from decomposed long-slit spectra were fairly robustagainst uncertainties in the decomposition parameters used in thefits.

Finally, Fig. 21 shows the derived star formation histories for eachsimulated galaxy. While these plots do show some scatter, especiallyin the case of 7443-12701, the general trends are consistent betweeneach model and with those presented in Fig. 17. The lower S/N ofthe decomposed spectra derived from the simulated galaxies is themost likely reason for this scatter. The systematically lower ages ofthe simulated discs in star formation history of the discs in Fig. 20are also reflected in the star formation histories of the simulateddiscs by extending to younger ages.

These final tests show that where the model gives a good fit to theoriginal galaxy, the decomposed spectra are a good representationof the star formation histories of each component within the galaxy.However, care must be taken when decomposing data cubes of lowS/N since the noise can propagate through to the final decomposedspectra, as shown here.

6 D ISCUSSION

We have presented BUDDI, a new method for applying two-dimensional bulge–disc decomposition to IFU data to cleanly sep-arate the light from the bulges and discs in order to study theirindependent star formation histories. The decomposed spectra canbe displayed as a data cube for each component, or as an integrated,one-dimensional spectrum. This technique builds upon earlier work,which decomposed multiwaveband photometry or long-slit spectra,to combine both the spectral and spatial information in the decom-position. As a result, a cleaner separation of the bulge and disc stellarpopulations can be achieved, leading to a better understanding oftheir independent star formation histories and thus how galaxiesevolve.

Since IFU data cubes typically have a smaller field of view thanimaging data, a series of tests have been carried out on both sim-ulated and real MaNGA data in order to determine the reliabilityof the decomposition when the outskirts of the galaxy may not be

visible. These tests found that in cases where the galaxy can bewell modelled by a single or double Sersic model, the best fit us-ing the MaNGA field of view for the 127, 91 and 61 fibre IFUs iscomparable to that using the larger field of view typically availablefor imaging data. This result suggests that by using the full spec-tral information through the data cube and the increased signal tonoise over the whole data set when applying simultaneous fits, thefit to each galaxy is reliable and can accurately separate the spectrafrom each component. Additional tests were carried out to comparethe single-band fits from GALFIT with the simultaneous fitting ofGALFITM. These tests found that GALFITM improved the extraction ofinformation, particularly at low S/N, which is consistent with thecomparisons carried out by Vika et al. (2013) on a smaller numberof wavebands.

In order to demonstrate the capabilities and applications of thisnew technique, a preliminary stellar populations analysis is pre-sented for two early-type galaxies from the MaNGA commission-ing sample. The light- and mass-weighted stellar populations weremeasured for both the decomposed bulge and disc spectra and for theradially binned data cubes after obliterating the kinematics but be-fore decomposition. The results from the decomposed spectra werefound to be less noisy than and consistent with those from the radi-ally binned data cubes, again showing that the decomposition of thistype of data is reliable for a range of galaxy morphologies and thuscan be useful for detailed studies of galaxy evolution through thebuild-up of the different components. Similarly, the results derivedfrom decomposing a series of simulated data cubes created from thedecomposed spectra for 7443-12701 and 7443-9102 were found tobe reproducible and consistent with the measurements from thesegalaxies, further reflecting the reliability of the technique when anappropriate model is selected for the fit.

The tests and analysis presented in this paper already illustratethe potential power of applying profile-fitting techniques to IFUdata, but there is still room for development. For a more completeanalysis, the technique could be applied to other data sets such asCALIFA or MUSE data. Additionally, one could use the residualdata cubes, created by subtracting the best fit from the original data,to analyse the stellar populations in non-smooth structures suchas spiral arms. The same analysis could also be carried out usingthe new non-parametric feature within GALFITM, which is still beingtested by the MegaMorph team.

It would also be useful to make better use of the kinematics infor-mation that is currently obliterated in this technique. For example,any emission features present could be modelled and subtracted toallow for a better measurement of the stellar populations in currentlystar-forming galaxies, thus extending this technique to a wider rangeof galaxy types.

While the analysis presented in this paper is able to measurecolour gradients within each component through the variation in theeffective radius of that component with radius (Johnston et al. 2012;Vulcani et al. 2014; Kennedy et al. 2015), the degeneracy betweenage and metallicity prevents this information from being translatedinto stellar population gradients. However, in Johnston et al. (2012),we showed that by allowing the effective radii to be free with wave-length in the fits of long-slit spectra, the line index gradients couldbe measured and used to derive gradients in the ages and metallic-ities. This idea could be applied to the analysis above by repeatingthe fits over smaller wavelength regions centred on the spectral fea-ture of interest and reducing the constraints on the effective radii,which could then be translated into age and metallicity gradientswithin each component. Such an improvement in the technique de-scribed here could significantly increase the amount of information

MNRAS 465, 2317–2341 (2017)




Dow

nloaded from



we could learn about the independent star formation histories ofeach component, and the cost of larger error bars due to using lessdata.

By isolating the bulge and disc stellar populations and the gas andstellar kinematics in this way, we plan to address open questionsabout their evolution. For example, one could go beyond derivingthe star formation histories of the bulge and disc as a whole, andinstead analyse how the star formation was triggered and truncatedin the inner and outer regions of each component. Positive agegradients with radius within the discs of S0s could reflect a gasstripping scenario leading to the truncation of star formation fromthe outside in (Larson, Tinsley & Caldwell 1980; Bekki, Shioya& Couch 2002), while flatter gradients may correspond to interac-tions with neighbouring galaxies leading to a final episode of starformation throughout the disc (Mihos & Hernquist 1994). Simi-larly, negative age gradients within bulges could indicate that thebulge was built up through multiple minor mergers (Kormendy &Kennicutt 2004), while positive age gradients would reflect a sce-nario where gas was funnelled into the centre where it fuelled morerecent star formation (Friedli & Benz 1995).

All these ideas, however, are well beyond the scope of this paperand will be addressed in future publications.

AC K N OW L E D G E M E N T S

We would like to thank Vladimir Avila-Reese for useful discussionsabout the technique and future applications of the technique pre-sented in this paper. We would also like to thank the anonymousreferee for their useful comments that helped improve this paper.

EJJ acknowledges support from the Marie Curie Actions ofthe European Commission (FP7-COFUND) and the Science andTechnology Facilities Council (STFC). KB acknowledges sup-port from the World Premier International Research Center Ini-tiative (WPI Initiative), MEXT, Japan and by JSPS KAKENHIGrant no. 15K17603. MAB acknowledges support from NSFAST-1517006.

Funding for the SDSS-IV has been provided by the Alfred P.Sloan Foundation, the US Department of Energy Office of Science,and the Participating Institutions. SDSS-IV acknowledges supportand resources from the Center for High-Performance Computing atthe University of Utah. The SDSS website is www.sdss.org.

SDSS-IV is managed by the Astrophysical Research Consor-tium for the Participating Institutions of the SDSS Collaborationincluding the Brazilian Participation Group, the Carnegie Institu-tion for Science, Carnegie Mellon University, the Chilean Participa-tion Group, the French Participation Group, Harvard–SmithsonianCenter for Astrophysics, Instituto de Astrofısica de Canarias, TheJohns Hopkins University, Kavli Institute for the Physics and Math-ematics of the Universe (IPMU)/University of Tokyo, LawrenceBerkeley National Laboratory, Leibniz Institut fur AstrophysikPotsdam (AIP), Max-Planck-Institut fur Astronomie (MPIA Hei-delberg), Max-Planck-Institut fur Astrophysik (MPA Garching),Max-Planck-Institut fur Extraterrestrische Physik (MPE), NationalAstronomical Observatory of China, New Mexico State Univer-sity, New York University, University of Notre Dame, ObservatarioNacional / MCTI, The Ohio State University, Pennsylvania StateUniversity, Shanghai Astronomical Observatory, United KingdomParticipation Group, Universidad Nacional Autonoma de Mexico,University of Arizona, University of Colorado Boulder, Universityof Oxford, University of Portsmouth, University of Utah, Univer-sity of Virginia, University of Washington, University of Wisconsin,Vanderbilt University, and Yale University.

This research made use of Montage. It is funded by the NationalScience Foundation under Grant Number ACI-1440620, and waspreviously funded by the National Aeronautics and Space Adminis-tration’s Earth Science Technology Office, Computation Technolo-gies Project, under Cooperative Agreement Number NCC5-626 be-tween NASA and the California Institute of Technology.

R E F E R E N C E S

Abazajian K. N. et al., 2009, ApJS, 182, 543Aguerri J. A. L., Iglesias-Paramo J., Vilchez J. M., Munoz-Tunon C., 2004,

AJ, 127, 1344Aihara H. et al., 2011, ApJS, 193, 29Allen P. D., Driver S. P., Graham A. W., Cameron E., Liske J., de Propris

R., 2006, MNRAS, 371, 2Bacon R. et al., 2010, in McLean I. S., Ramsay S. K., Takami H., eds, Proc.

SPIE Conf. Ser. Vol. 7735, Ground-Based and Airborne Instrumentationfor Astronomy III. SPIE, Bellingham, p. 773508

Barway S., Wadadekar Y., Kembhavi A., Mayya Y. D., 2009, MNRAS, 394,1991

Beckman J., Peletier R., Knapen J., Corradi R., Gentet L., 1996, ApJ, 467,175

Beifiori A., Maraston C., Thomas D., Johansson J., 2011, A&A, 531, A109Bekki K., Shioya Y., Couch W. J., 2002, ApJ, 577, 651Bothun G. D., Gregg M. D., 1990, ApJ, 350, 73Bundy K. et al., 2015, ApJ, 798, 7Burstein D., 1979, ApJ, 234, 829Byun Y. I., Freeman K. C., 1995, ApJ, 448, 563Cameron E., Driver S. P., Graham A. W., Liske J., 2009, ApJ, 699, 105Cappellari M., Copin Y., 2003, MNRAS, 342, 345Cappellari M., Emsellem E., 2004, PASP, 116, 138de Jong R. S., 1996a, A&AS, 113, 134de Jong R. S., 1996b, A&A, 313, 377Disney M., Davies J., Phillipps S., 1989, MNRAS, 239, 939Djorgovski S., Davis M., 1987, ApJ, 313, 59Drory N. et al., 2015, AJ, 149, 77Falcon-Barroso J., Sanchez-Blazquez P., Vazdekis A., Ricciardelli E.,

Cardiel N., Cenarro A. J., Gorgas J., Peletier R. F., 2011, A&A, 532,A95

Ferrarese L. et al., 2006, ApJS, 164, 334Friedli D., Benz W., 1995, A&A, 301, 649Gonzalez J. J., 1993, PhD thesis, Univ. CaliforniaGonzalez Delgado R. M. et al., 2015, A&A, 581, A103Graham A. W., 2001, AJ, 121, 820Graham A. W., Worley C. C., 2008, MNRAS, 388, 1708Gunn J. E. et al., 2006, AJ, 131, 2332Hamabe M., Kormendy J., 1987, in de Zeeuw P. T., ed., Proc. IAU Symp.

127, Structure and Dynamics of Elliptical Galaxies. Reidel, Dordrecht,p. 379

Haußler B. et al., 2007, ApJS, 172, 615Haußler B. et al., 2013, MNRAS, 430, 330Head J. T. C. G., Lucey J. R., Hudson M. J., Smith R. J., 2014, MNRAS,

440, 1690Hudson M. J., Stevenson J. B., Smith R. J., Wegner G. A., Lucey J. R.,

Simard L., 2010, MNRAS, 409, 405Huertas-Company M., Aguerri J. A. L., Bernardi M., Mei S., Sanchez

Almeida J., 2011, A&A, 525, A157Johnston E. J., Aragon-Salamanca A., Merrifield M. R., Bedregal A. G.,

2012, MNRAS, 422, 2590Johnston E. J., Aragon-Salamanca A., Merrifield M. R., 2014, MNRAS,

441, 333Kannappan S., Guie J., Baker A., 2009, AJ, 138, 579Kelvin L. S. et al., 2012, MNRAS, 421, 1007Kennedy R. et al., 2015, MNRAS, 454, 806Kent S. M., 1985, ApJS, 59, 115Ko J., Im M., 2005, J. Korean Astron. Soc., 38, 149Kormendy J., 1977, ApJ, 218, 333

MNRAS 465, 2317–2341 (2017)




Dow

nloaded from

http://www.sdss.org



Kormendy J., Kennicutt R. C., Jr, 2004, ARA&A, 42, 603Kuntschner H. et al., 2006, MNRAS, 369, 497La Barbera F., De Carvalho R. R., De La Rosa I. G., Gal R. R., Swindle R.,

Lopes P. A. A., 2010, AJ, 140, 1528Lackner C. N., Gunn J. E., 2012, MNRAS, 421, 2277Lange R. et al., 2015, MNRAS, 447, 2603Larson R. B., Tinsley B. M., Caldwell C. N., 1980, ApJ, 237, 692Laurikainen E., Salo H., Buta R., Knapen J. H., 2007, MNRAS, 381, 401Law D. R. et al., 2015, AJ, 150, 19Law D. R. et al., 2016, AJ, 152, 83Lintott C. et al., 2011, MNRAS, 410, 166MacArthur L. A., Courteau S., Holtzman J. A., 2003, ApJ, 582, 689McDermid R. M. et al., 2015, MNRAS, 448, 3484Maltby D. T. et al., 2012, MNRAS, 419, 669Mendel J. T., Simard L., Palmer M., Ellison S. L., Patton D. R., 2014, ApJS,

210, 3Michard R., Poulain P., 2000, A&AS, 141, 1Mihos J. C., Hernquist L., 1994, ApJ, 425, L13Mollenhoff C., 2004, A&A, 415, 63Mollenhoff C., Heidt J., 2001, A&A, 368, 16Oohama N., Okamura S., Fukugita M., Yasuda N., Nakamura O., 2009, ApJ,

705, 245Pahre M. A., Djorgovski S. G., de Carvalho R. R., 1998a, AJ, 116, 1591Pahre M. A., de Carvalho R. R., Djorgovski S. G., 1998b, AJ, 116, 1606Peletier R. F., Balcells M., 1996, AJ, 111, 2238Peng C. Y., Ho L. C., Impey C. D., Rix H.-W., 2002, AJ, 124, 266Peng C. Y., Ho L. C., Impey C. D., Rix H.-W., 2010, AJ, 139, 2097Pforr J., Maraston C., Tonini C., 2012, MNRAS, 422, 3285Poggianti B. M. et al., 2001, ApJ, 563, 118Pohlen M., Dettmar R.-J., Lutticke R., Aronica G., 2002, A&A, 392, 807Pompei E., Natali G., 1997, A&AS, 124, 129Press W. H., Teukolsky S. A., Vetterling W. T., Flannery B. P., 1992, Numeri-

cal Recipes in FORTRAN. The Art of Scientific Computing. CambridgeUniv. Press, Cambridge

Rawle T. D., Smith R. J., Lucey J. R., Swinbank A. M., 2008, MNRAS, 389,1891

Rodrıguez Del Pino B., Bamford S. P., Aragon-Salamanca A., Milvang-Jensen B., Merrifield M. R., Balcells M., 2014, MNRAS, 438, 1038

Sanchez S. F. et al., 2012, A&A, 538, A8Sanchez-Blazquez P. et al., 2006, MNRAS, 371, 703Seigar M. S., James P. A., 1998, MNRAS, 299, 685Shaw M. A., Gilmore G., 1989, MNRAS, 237, 903Sil’Chenko O. K., 2006, Astron. Astrophys. Trans., 25, 199Sil’chenko O. K., Proshina I. S., Shulga A. P., Koposov S. E., 2012, MNRAS,

427, 790Simard L. et al., 2002, ApJS, 142, 1Simard L., Mendel J. T., Patton D. R., Ellison S. L., McConnachie A. W.,

2011, ApJS, 196, 11Smee S. A. et al., 2013, AJ, 146, 32Tabor M., Merrifield M., Aragon-Salamanca A., Cappellari M., Bamford

S. P., Johnston E., 2016, preprint (arXiv:e-prints)Terndrup D. M., Davies R. L., Frogel J. A., DePoy D. L., Wells L. A., 1994,

ApJ, 432, 518Thomas D., Davies R. L., 2006, MNRAS, 366, 510Thomas D., Maraston C., Bender R., 2003, MNRAS, 339, 897Thomas D., Maraston C., Johansson J., 2011, MNRAS, 412, 2183Trager S. C., Faber S. M., Worthey G., Gonzalez J. J., 2000, AJ, 119,

1645Trujillo I., Asensio Ramos A., Rubino-Martın J. A., Graham A. W., Aguerri

J. A. L., Cepa J., Gutierrez C. M., 2002, MNRAS, 333, 510van der Kruit P. C., 1979, A&AS, 38, 15Vazdekis A., Sanchez-Blazquez P., Falcon-Barroso J., Cenarro A. J., Beasley

M. A., Cardiel N., Gorgas J., Peletier R. F., 2010, MNRAS, 404,1639

Vika M., Bamford S. P., Haußler B., Rojas A. L., Borch A., Nichol R. C.,2013, MNRAS, 435, 623

Vika M., Bamford S. P., Haußler B., Rojas A. L., 2014, MNRAS, 444, 3603Vulcani B. et al., 2014, MNRAS, 441, 1340Worthey G., 1994, ApJS, 95, 107Worthey G., Ottaviani D. L., 1997, ApJS, 111, 377Worthey G., Faber S. M., Gonzalez J. J., Burstein D., 1994, ApJS, 94, 687Yan R. et al., 2016, AJ, 151, 8Zhao G.-B. et al., 2016, MNRAS, 457, 2377

This paper has been typeset from a TEX/LATEX file prepared by the author.

MNRAS 465, 2317–2341 (2017)




Dow

nloaded from

http://arxiv.org/abs/e-prints


sdss-iv manga: bulge–disc decomposition of ifu data cubes … · 2017-02-18 · evelyn j....

Documents